Question

How many terms are in the expansion (a + b)18.

Answer 1

Each term will be a power of \(a\) (or \(b\), depending on how you look at it).

WIth respect to \(a\), the first term will have degree 18, i.e. \(a^{18}=a^{18}b^0\), and the last term will have degree 0, i.e. \(a^0b^{18}=b^{18}\).

The exponent of \(a\) ranges from 0 to 18, and so there are 19 terms (because there are 19 numbers in the sequence 0,1,...,17,18).